Core Connections, Course 3

Core Connections, Course 3 is the third of a three-year sequence of courses designed to prepare students for a rigorous college preparatory high school mathematics course.

On a daily basis, students in Core Connections, Course 3 use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Under teacher guidance, students learn in collaboration with others while sharing information, expertise, and ideas. The course helps students to develop multiple strategies to solve problems and to recognize the connections between concepts. The lessons in the course meet all of the content standards and embed the “Mathematical Practices” of the Common Core State Standards released in June 2010. Read More...

Upon completion of this course, students should be able to:

Represent a linear function with a graph, table, rule, and context and create any representation when provided one of the others.

Solve systems of equations by using tables and graphs.

Symbolically manipulate expressions to solve problems including those with fractional coefficients.

Solve contextual word problems using multiple strategies, including making tables, looking for patterns, drawing diagrams, and creating a table of guesses to assist with writing and solving a variable equation.

Describe various geometric transformations on a coordinate grid.

Represent data using scatterplots and describe associations.

Collect and analyze data and make predictions based on the trend of the data.

Compare ratios and calculate unit rates and slope ratios.

Analyze the slope of a line graphically, numerically, and contextually.

Recognize and solve problems involving proportional relationships.

Graph and analyze non-linear functions.

Recognize and use the properties of similar figures to solve problems.

Use the Pythagorean Theorem and its converse to solve problems in two and three dimensions.

Use square roots and cube roots.

Represent and simplify expressions using positive and negative exponents.

Represent and compare large and small numbers using standard and scientific notation.

Perform operations with numbers represented in scientific notation.

Use the relationships between angles created by parallel lines with transversals and the Triangle Angle Sum Theorem to solve problems.

LESSON STRUCTURE

The Core Connections courses are built on rich, meaningful problems and investigations that develop conceptual understanding of the mathematics and establish connections among different concepts. The lesson problems are non-routine and team-worthy, requiring strategic problem solving and collaboration. Throughout the course, students are encouraged to justify their reasoning, communicate their thinking, and generalize patterns. Read More...

In each lesson students work collaboratively in study teams on challenging problems. The teacher is continuously providing structure and direction to teams by asking questions and giving clarifying instructions. The teacher gives targeted lectures or holds whole-class discussions when appropriate. The teacher has the freedom to decide the level of structure or open-endedness of each lesson. While students are in teams, the teacher checks for understanding by questioning students’ thinking and asking students to justify their solutions. Questioning is informative to both the teacher and the student as it guides the students to the learning target. At the close of each lesson, the teacher ensures that the students understand the big mathematical ideas of the lesson.

The homework in the “Review & Preview” section of each lesson includes mixed, spaced practice, and prepares students for new topics. The homework problems give students the opportunity to apply previously-learned concepts to new contexts. By solving the same types of problems in different ways, students deepen their understanding. CPM offers open access homework support at homework.cpm.org. Read Less...

COURSE STRUCTURE

Chapters are divided into sections that are organized around core topics. Within each section, lessons include activities, challenging problems, investigations and practice problems. Teacher notes for each lesson include a “suggested lesson activity” section with ideas for lesson introduction, specific tips and strategies for lesson implementation to clearly convey core ideas, and a means for bringing the lesson to closure. Read More...

Core ideas are synthesized in “Math Notes” boxes throughout the text. These notes are placed in a purposeful fashion, often falling one or more lessons after the initial introduction of a concept. This approach allows students time to explore and build conceptual understanding of an idea before they are presented with a formal definition or an algorithm or a summary of a mathematical concept. “Math Notes” boxes include specific vocabulary, definitions and instructions about notation, and occasionally interesting extensions or real-world applications of mathematical concepts.

Learning Log reflections appear periodically at the end of lessons to allow students to synthesize what they know and identify areas that need additional explanation. Toolkits are provided as working documents in which students write Learning Logs, interact with Math Notes and create other personal reference tools.

Each chapter offers review problems in the chapter closure: typical problems that students can expect on an assessment, answers, and support for where to get help with the problem. Chapter closure also includes lists of Math Notes and Learning Logs, key vocabulary in the chapter, and an opportunity to create structured graphic organizers.

The books include “Checkpoints” that indicate to students where fluency with a skill should occur. Checkpoints offer examples with detailed explanations, in addition to practice problems with answers.

In addition, CPM provides a Parent Guide with Extra Practice available for free download at cpm.org or in booklet form for purchase. In addition to practice problems with answers, the Parent Guide with Extra Practice provides examples with detailed explanations and guidance for parents and tutors.

Technology is used in the course to allow students to see and explore concepts after they have developed some initial conceptual understanding. Ideally, classes have access to a computer lab with computers for pairs of students to use the dynamic tools that provide students with a deeper understanding of the concepts involved.
A classroom computer equipped with projection technology suffices, but does not allow students to explore individually.
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